Solve (-2/3a^4b^3):(-3ab)=

$$( - \frac { 2 } { 3 } a ^ { 4 } b ^ { 3 } ) : ( - 3 a b ) =$$

Evaluate

$$\frac{2b^{2}a^{3}}{9}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-\frac{2}{3}\right)^{1}a^{4}b^{3}}{\left(-3\right)^{1}a^{1}b^{1}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\left(-\frac{2}{3}\right)^{1}}{\left(-3\right)^{1}}a^{4-1}b^{3-1}$$

Subtract 1 from 4.

$$\frac{\left(-\frac{2}{3}\right)^{1}}{\left(-3\right)^{1}}a^{3}b^{3-1}$$

Subtract 1 from 3.

$$\frac{\left(-\frac{2}{3}\right)^{1}}{\left(-3\right)^{1}}a^{3}b^{2}$$

Divide -\frac{2}{3} by -3.

$$\frac{2}{9}a^{3}b^{2}$$

Differentiate w.r.t. a

$$\frac{2\left(ab\right)^{2}}{3}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\left(-\frac{\frac{2b^{3}}{3}}{-3b}\right)a^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2b^{2}}{9}a^{3})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3\times \frac{2b^{2}}{9}a^{3-1}$$

Do the arithmetic.

$$\frac{2b^{2}}{3}a^{2}$$